3542 JOURNAL OF CLIMATE VOLUME 20 Decadal Climate Variability: Is There a Tidal Connection? RICHARD D. RAY NASA Goddard Space Flight Center, Greenbelt, Maryland (Manuscript received 14 June 2006, in final form 8 November 2006) ABSTRACT A possible connection between oceanic tides and climate variability arises from modulations in tidally induced vertical mixing. The idea is reexamined here with emphasis on near-decadal time scales. Occasional extreme tides caused by unusually favorable alignments of the moon and sun are unlikely to influence decadal climate, since these tides are of short duration and, in fact, are barely larger than the typical spring tide near lunar perigee. The argument by Keeling and Whorf in favor of extreme tides is further handi- capped by an insufficiently precise catalog of extreme tides. A more plausible connection between tides and near-decadal climate is through “harmonic beating” of nearby tidal spectral lines. The 18.6-yr modulation of diurnal tides is the most likely to be detectable. Possible evidence for this is reviewed. Some of the most promising candidates rely on temperature data in the vicinity of the North Pacific Ocean where diurnal tides are large, but definitive detection is hindered by the shortness of the time series. Paleoclimate temperature data deduced from tree rings are suggestive, but one of the best examples shows a phase reversal, which is evidence against a tidal connection. 1. Introduction including deep-water formation (e.g., Lee et al. 2006). Moreover, the meridional overturning itself is possibly My title is borrowed from Munk et al. (2002), except driven in part by deep-ocean tidal mixing. Munk and their “millennial” is here “decadal.” The Munk et al. Wunsch (1998) lay out the main ideas and a very rough study was stimulated in large part by two papers by energy budget. Egbert and Ray (2000) show that the Keeling and Whorf (1997, 2000), who argued that glob- barotropic tide is energetically capable of depositing al temperature data show significant inverse correla- the requisite energy into the deep ocean, and many tions with times of maximum tidal forces. In the Keel- current studies of deep-ocean internal tides are at- ing–Whorf view, large tides induce enhanced oceanic tempting to unravel the mechanisms and energetics in vertical mixing, with associated perturbations to global better detail (e.g., Rudnick et al. 2003). surface temperatures and climate. Munk et al. took a Notwithstanding the existence of tidally induced mix- dim view of any such tidal effect working at millennial ing, however, it is difficult to see how occasional ex- time scales, but they concluded that the Keeling–Whorf treme tides–or tidal “events,” as labeled by Keeling and proposal was “the most likely among unlikely candi- Whorf (1997, hereinafter KW97)–which are of very dates.” short duration and only marginally larger than typical The connection between tides and vertical mixing at spring tides, could affect climate on decadal (or longer) shorter time scales is more firmly established, and pos- time scales. Yet there continues to be a steady stream of sible climatic influences appear more conceivable. papers published along these lines, many of them find- Tidal mixing in shallow seas is a common and well- ing supposed correlations between occasional extreme studied phenomenon, with fortnightly oscillations aris- tides and various decadal-scale climatic variables. Be- ing from the spring–neap cycle apparent in many loca- cause the Keeling–Whorf study is one of the more in- tions. Mixing in key regions, such as the Labrador Sea, fluential of these efforts, its arguments are worth ex- is capable of influencing larger-scale ocean circulation, amining in greater depth. When that is done, as shown below, the KW97 hypothesis appears even weaker than Corresponding author address: Richard D. Ray, NASA God- one might have initially thought. dard Space Flight Center, Code 698, Greenbelt, MD 20771. The material in sections 3 and 4 is developed primar- E-mail: [email protected] ily to address the KW97 paper. But those calculations DOI: 10.1175/JCLI4193.1 Unauthenticated | Downloaded 09/27/21 07:17 AM UTC JCLI4193 15 JULY 2007 R A Y 3543 FIG. 1. (a) Monthly mean surface temperature anomalies from Jones and Moberg (2003). (b) Filtered monthly mean temperature data (solid curve) based on nine dominant frequencies appearing in the original time series, according to Keeling and Whorf (1997). Gray vertical bars denote times of extreme tidal events, also according to Keeling and Whorf. Stars denote times at which the mean longitude of the moon’s ascending node passed the equinox, resulting in generally larger diurnal tides (see appendix B). naturally lend themselves to related connections, or garding the nodal cycle, typically as confusion between possible connections, between tides and climate. To an- the nodal modulations of short-period (daily) tides and swer the question in our title with anything but a nega- the 18.6-yr node tide itself, appendix B offers a short tive, the most promising of these connections is inves- tutorial on the nodal regression and its tidal conse- tigated, with a generously flexible definition of “cli- quences. mate” to include even very localized atmospheric effects. The most promising link involves “harmonic 2. Keeling–Whorf hypothesis beating” (Munk et al. 2002) from the moon’s 18.6-yr nodal cycle and its modulation of short-period tides KW97 began with monthly mean, global surface tem- (Loder and Garrett 1978). It is quite analogous to the perature anomalies as described by Jones et al. (1999) spring–neap fortnightly modulation readily observed in and shown here in Fig. 1a. They filtered these data in many shallow seas. Thus, in this case the physical several different ways to reveal variability in the near- mechanism via mixing between tides and decadal (or decadal band. The filtered time series adopted here is nearly bidecadal) variability appears on somewhat similar to the one that KW97 generally emphasized in firmer ground, although details remain murky. Evi- terms of correlations with tides. It is based on KW97’s dence for an 18.6-yr effect in historical climate records maximum entropy spectrum analysis that suggested is intriguingly suggestive but by no means completely nine dominant frequencies in the period range between convincing. These matters are discussed in sections 5–7, 6.05 to 31.4 yr. The monthly data are fit by least squares primarily as a brief review of work by others. Because to sinusoids at these identified frequencies (plus a low- the climate literature abounds with misconceptions re- degree polynomial to absorb the main secular trends). Unauthenticated | Downloaded 09/27/21 07:17 AM UTC 3544 JOURNAL OF CLIMATE VOLUME 20 The resulting nine-term sinusoidal series is shown in Fig. 1b. The curve in Fig. 1b corresponds closely to the “low frequency/spectral” curve in KW97’s Fig. 7. The vertical gray bars in Fig. 1b delineate the so- called tidal events of KW97. These are times identified as having unusually large tidal forces; they were ex- tracted from a compilation by Wood (1986). As KW97 emphasized, there is some tendency for the tidal events to fall near times of global low temperatures, although there are also obvious exceptions. In an attempt to be more objective, a statistical test has here been devised, with details given in appendix A. The result is that the null hypothesis of complete independence between KW97’s tidal events and the temperature oscillations can be rejected at the 5% level but not at the 1% level.1 Because the entire KW97 hypothesis, as well as oth- ers of a similar nature, rests upon these coincidences between tidal event times and filtered temperature ex- tremes, it is important to understand in detail how these tidal events are determined and how anomalous (or not) they actually are. This is discussed in the following section. FIG. 2. Geometry of earth–moon–sun determining total tide- generating force. Spring tides occur when ␺ Ϸ 0° (new moon) or ␺ Ϸ 180° (full moon). Maximum tidal force occurs at the point P, which is offset from the sublunar point by the angle ␦. Because the 3. Times of maximum tidal force lunar potential dominates the solar, ␦ is always less than 16°. The tidal events used by KW97, corresponding to times of unusually large tidal forces on the earth, are semidiurnal components, see section 5.) The total po- extracted from Table 16 of Wood (1986). They are not tential at point P is given by actually based on direct calculations of the tidal forces but rather on a particular angular velocity of the moon, ͑ ͒ ϭ ͑ ͒ ϩ ͑ ͒ V P VM P VS P , which is taken as a proxy for the tidal force. Since the calculation of the actual force (or potential) is straight- where the lunar potential is forward, there appears no reason to resort to such a proxy, especially since the identified events turn out to GM a 2 a 3 ͑ ͒ ϭ mͭͩ ͪ ͑ ␦͒ ϩ ͩ ͪ ͑ ␦͒ VM P P2 cos P3 cos be sensitively dependent on the precision of the calcu- Rm Rm Rm lations. In this section, the times of maximum tidal a 4 force (or potential) are recomputed and it is shown how ϩ ͩ ͪ ͑ ␦͒ͮ ͑ ͒ P4 cos , 1 so-called extreme events are identified. Rm We assume a rigid, spherical earth. Figure 2 defines where G is the Newtonian constant, M is the lunar all the astronomical quantities required for the calcula- m mass, a is the mean equatorial radius of the earth, and tion of the maximum tidal potential, which occurs at the P (␮) is a Legendre function of degree n.